A 4.15-volt battery is connected across a parallel-plate capacitor. Illuminating

Question

A 4.15-volt battery is connected across a parallel-plate capacitor. Illuminating the plate with ultraviolet light causes electrons to be emitted from the plates with a speed of 1.76 x 10^6 m/s.

(a) Suppose electrons are emitted near the center of the negative plate and travel perpendicular to that plate toward the opposite plate. Find the speed of the electrons when they reach the positive plate.

(b) Suppose instead that electrons are emitted perpendicular to the psitive plte. Find their speed when they reach the negative plate.

Explanation / Answer

A)

initial kinetic energy:

Ki = 0.5 m vi^2 = 0.5 * 9.109e-31 * 1.76e6*1.76e6 = 1.4108e-18 J

electrical energy:

E = q V = 1.6e-19 * 4.15 = 6.64e-19 J

Kf = Ki - E = 1.4108e-18 - 6.64e-19 = 7.468e-19 J

v = 2K/m = (2*7.468e-19/9.109e-31) = 1.28e6 m/s

B)

initial kinetic energy:

Ki = 0.5 m vi^2 = 0.5 * 9.109e-31 * 1.76e6*1.76e6 = 1.4108e-18 J

electrical energy:

E = q V = 1.6e-19 * 4.15 = 6.64e-19 J

Kf = Ki + E = 1.4108e-18 + 6.64e-19 = 20.748e-19 J

v = 2K/m = (2*20.748e-19/9.109e-31) = 2.13e6 m/s

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